the former being obvious e.g. from Theorem REF (b), whereas the latter holds true by [1]}.
Noting that \(\mu ,\mu ^A\in \Gamma _{A,\mu }^+\) , we conclude by combining (REF ) with (REF ) that there are actually infinitely many measures of minimum total mass in \(\Gamma _{A,\mu }^+\) , for so is every measure of the form \(a\mu +b\mu ^A\) , where \(a,b\in [0,1]\)  and \(a+b=1\) .

